Factoring and simplifying rational expresssions

Woo boy. I'm learning this at home, on my own, and I am struggling. Every time I sit down at my textbook I want to throw it across the room. I'm looking at purplemath.com for another perspective on how to do this and it's helping but it's still slow going.

I am still struggling with taking an expression like:

x2 + 2x - 15

and factoring it. It's a lot of guess work and I get very irritated and frustrated with that.

(x-3)(x+5) <--- I know this because I have the answer. LOL

It is not intuitive for me to look at the expression above and come to these factor. I know it will just take practice, but right now that doesn't console me much. ;)

I want a simple formula that guides me in how to factor these, instead of trying to figure out what multiples of -15 are going to help me find +2. Bah! I know how to do it. I just don't like doing it.

I'm afraid that when asked to 'simplify' or 'factor' an expression or equation that I will not be sure what I'm being asked, and that I will do the wrong thing. I have to learn this in a way that leaves me comfortable and confident, like addition and subtraction.

I got it :)

I needed to flush out the problem more. I made the mistake of looking at the problem and thinking that it was in a final form and it's not. :D Yahoo!

Linear Equations and Parallel Lines

Problem:
(Section 4.4 #41)

3x +5y = 9
6x = -10y +9

How are these lines parallel? The slope of the first is 3. The slope of the second is 6. At least that's how it appears. (Bear in mind I'm learning this as I go, so if I'm clearly missing something, don't be shy.

What am I missing? Do I need to solve for x or y?

Still working on it.